Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Strong Convergence Theorems of the CQ Method for Nonexpansive Semigroups Huimin He and Rudong Chen | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 59735 8 pages doi 2007 59735 Research Article Strong Convergence Theorems of the CQ Method for Nonexpansive Semigroups Huimin He and Rudong Chen Received 25 January 2007 Accepted 19 March 2007 Recommended by Jerzy Jezierski Motivated by T. Suzuki we show strong convergence theorems of the CQ method for nonexpansive semigroups in Hilbert spaces by hybrid method in the mathematical programming. The results presented extend and improve the corresponding results of Kazuhide Nakajo and Wataru Takahashi 2003 . Copyright 2007 H. He and R. Chen. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction and preliminaries Throughout this paper let H be a real Hilbert space with inner product and II II. We use xn x to indicate that the sequence xn converges weakly to x. Similarly xn - x will symbolize strong convergence. we denote by N and R the sets of nonnegative integers and nonnegative real numbers respectively. let C be a closed convex subset of a Hilbert space H and Let T C - C be a nonexpansive mapping . Tx - Tyll x - y II for all x y e C . We use Fix T to denote the set of fixed points of T that is Fix T x e C x Tx . We know that Fix T is nonempty if C is bounded for more details see 1 . In 2 Shioji and Takahashi introduce in a Hilbert space the implicit iteration 1 ftn xn anu 1 - an T s xnds n e N tn 0 Where an is a sequence in 0 1 tn is a sequence of positive real numbers divergent to TO for each t 0 and u e C. In 2003 Suzuki 3 is the first to introduce again in a Hilbert space the following implicit iteration process xn anU 1 - T tn xn n 1 2 Fixed Point Theory and Applications for the nonexpansive semigroup case. In 2005 Xu 4 established a Banach space version of the sequence of .
